An improved framework for approximating option prices with application to option portfolio hedging

As the price of the underlying asset changes over time, delta of the option changes and a gamma hedge is required along with delta hedge to reduce risk. This paper develops an improved framework to compute delta and gamma values with the average of a range of underlying prices rather than at the conventional fixed 'one point'. We find that models with time-varying volatility price options satisfactorily, and perform remarkably well in combination with the delta and delta-gamma approximations. Significant improvements are achieved for the GARCH model followed by stochastic volatility models. The new approach can ensure significant improvement in modelling option prices leading to better risk-management decision-making.